A produce of high-voltage switches projects demand (# switches) for the next calendar year to be Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Demand 600 800 1000 1500 2000 3000 3200 2200 1200 900 600 500 The plant runs for up to 160 regular time hours per month and can produce switches at a rate of 10 per hour (if less than 160 hours are used for switch production assume the hours can be used for other production. i.e. Profit is always $50 per switch, no matter how many RT hours are used.) Profit per switch = $50, and the inventory holding cost for one switch for one month is $5. Assume zero inventory at the beginning of January. The plant can run overtime at an added cost of $300 per hour for up to 200 hours of additional production time per month (the production rate is the same as regular time - 10 switches per hour). For each scenario below compute the annual profit for switch production. For each scenario include the monthly regular time production quantity used for switches, the overtime production quantity and cost, and the monthly inventory and inventory cost. (4 pts) Production meets demand exactly each month. (A LP is not needed. Set the production as the problem states.) b. (4 pts) Production each month is the same and set to the average monthly demand. In this case demand will not always be met. (A LP is not needed. Set the production as the problem states.) (2 pts) Formulate and solve a linear program to maximize annual profit. Show the details of your formulation (i.e. write out your LP formulation or show your Solver set up with a screen shot). Assume demand is always met. d. (Bonus: +1 pt extra credit) Formulate and solve a linear program to maximize annual profit. This time, production each month is the same and is the smallest quantity such that there are no shortages. Show the details of your formulation. (Hint: A linear program will be useful to solve this problem.) a. C.